My understanding of how hopscotch works is that youfirst compute all the (say) even-numbered points explicitly,and then all the others, also explicitly, but now thecalculation is effectively implicit because the secondseries uses the newly computed values.

We are dealing with a parabolic pde, u_t = u_{xx}

If the pde has a nonlinear term, my feeling is that this toois discretised explicitly in both series of steps, conformingto the hopscotch idea.

I am reading a paper in which the nonlinear term is handledimplicitly in the first, "explicit" series, using Newtoniteration; this is then followed by the second series, nowexplicitly. It seems to me that this is not adhering tothe hopscotch idea. Some experiments of mine using bothmethods lead to the same order wrt dT, close to unity, sothe Newton thing doesn't help.

Am I right; is the Newton iteration unnecessary or evenundesirable (in terms other than cpu time)?